Physics

Problem

A 2 kg cart is at

x=0\,\text{m}

and a 1 kg cart is at

x=4\,\text{m}

on a frictionless track. Without doing any calculations, describe how the position of the system’s center of mass will change if the 1 kg cart is moved to

x=2\,\text{m}

while the 2 kg cart remains fixed.

Intuitive explanation

The center of mass is the weighted average position of all objects in a system—heavier objects pull it toward them more strongly. Right now the 2 kg cart (at the origin) has twice the "weight" in that average as the 1 kg cart, so the center of mass sits closer to $x=0$ . When the 1 kg cart moves left from $x=4\,\text{m}$ toward $x=2\,\text{m}$ , it's moving toward the heavier cart, so the center of mass will shift left as well, but by a smaller amount than the 1 kg cart itself moves.

Intuitive explanation

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